How To Find The Hypotenuse Of A Rectangle

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A diagonal is a straight line that connects one corner of a rectangle to the opposite corner.^[1] A rectangle has two diagonals, and each is the same length.^[2] If you know side lengths of the rectangle, you tin easily find the length of the diagonal using the Pythagorean Theorem, since a diagonal divides a rectangle into two right triangles. If you don't know the side lengths, only you take other data, such as the surface area and perimeter, or the relationship between side lengths, some actress steps will allow you to find the length and width of the rectangle, and from there you can employ the Pythagorean Theorem to find the length and width of the diagonal.

1. 1

2. two

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3. 3

   Square the length and width, then add these numbers together. Remember, squaring a number means to multiply the number by itself.

4. four

   Accept the square root of each side of the equation. The easiest way to find a square root is to utilise a calculator. You tin can use an online computer if yous practise non have a scientific estimator.^[5] This volition give you the value of ${\displaystyle c}$ , which is the hypotenuse of the triangle, and the diagonal of the rectangle.

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1. 1

   Ready the formula for the area of a rectangle. The formula is ${\displaystyle A=lw}$ , where ${\displaystyle A}$ equals the area of the rectangle, ${\displaystyle l}$ equals the length of the rectangle, and ${\displaystyle w}$ equals the width of the rectangle.^[6]

2. 2

   Plug the area of the rectangle into the formula. Make sure yous substitute for the variable ${\displaystyle A}$ .

   • For example, if the area of the rectangle is 35 square centimeters, your formula will await like this: ${\displaystyle 35=lw}$ .

3. 3

   Rearrange the formula, finding a value for $$ w {\displaystyle w} . To do this, carve up both sides of the equation by ${\displaystyle l}$ . Set this value aside. Yous will plug it into the perimeter formula later on.

4. 4

   Gear up upwardly the formula for the perimeter of a rectangle. The formula is ${\displaystyle P=2(due west+50)}$ , where ${\displaystyle w}$ equals the width of the rectangle, and ${\displaystyle 50}$ equals the length of the rectangle.^[7]

5. 5

   Plug the value of the perimeter into the formula. Brand certain you substitute for the variable ${\displaystyle P}$ .

   • For example, if the perimeter of a rectangle is 24 centimeters, your formula will look like this: ${\displaystyle 24=ii(west+l)}$ .

6. 6

   Divide both sides of the equation by 2. This will requite yous the value of ${\displaystyle west+l}$ .

7. 7

   Plug the value of $$ westward {\displaystyle west} into the equation. Utilize the value you found past rearranging the formula for area.

8. 8

   Cancel out the fraction in the equation. To do this, multiply both sides of the equation by ${\displaystyle l}$ .

9. 9

   Set the equation to 0. To practice this, subtract the first-degree term from both sides of the equation.

10. 10

    Reorder the equation by social club of terms. This ways the term with the exponent will be first, followed by the term with the variable, followed by the constant. When reordering, make sure you go on the advisable positive and negative signs. Yous should note that the equation is now set every bit a quadratic equation.

11. 11

12. 12

    Find the values of $$ l {\displaystyle fifty} . To do this, set up each term to cipher and solve for the variable. You volition observe two solutions, or roots, to the equation. Since you are working with a rectangle, the 2 roots will be the width and length of your rectangle.

13. 13

14. xiv

    Plug the width and length into the formula. It doesn't matter which value y'all use for which variable.

    • For example, if you lot found the width and length of the rectangle are 5 cm and seven cm, your formula will look like this: ${\displaystyle five^{2}+vii^{2}=c^{2}}$ .

15. fifteen

    Square the width and length, and then add together these numbers together. Call back, squaring a number ways to multiply the number past itself.

16. 16

    Have the square root of each side of the equation. The easiest way to find a square root is to use a calculator. You lot can apply an online calculator if y'all do not take a scientific calculator.^[10] This volition requite you the value of ${\displaystyle c}$ , which is the hypotenuse of the triangle, and the diagonal of the rectangle.

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1. 1

   Write a formula explaining the relationship between the side lengths. ^[11] You tin can isolate the length ( ${\displaystyle 50}$ ) or the width ( ${\displaystyle w}$ ). Set this formula bated. You will plug it into the area formula later.

2. two

3. 3

   Plug the area of the rectangle into the formula. Brand certain you substitute for the variable ${\displaystyle A}$ .

   • For example, if the surface area of the rectangle is 35 foursquare centimeters, your formula volition look like this: ${\displaystyle 35=lw}$ .

4. iv

   Plug the relational formula for the length (or width) into the formula. Since yous are working with a rectangle, it doesn't thing whether you lot work with the ${\displaystyle l}$ or ${\displaystyle w}$ variable.

5. five

   Set a quadratic equation. To do this, use the distributive property to multiply the terms in parentheses, then set the equation to 0.

6. 6

7. 7

   Discover the values of $$ l {\displaystyle l} . To practise this, set each term to null and solve for the variable. You volition find 2 solutions, or roots, to the equation.

8. 8

   Plug the value of the length (or width) into your relationship formula. This will give you the length of the other side of the rectangle.

9. 9

10. 10

    Plug the width and length into the formula. Information technology doesn't affair which value you lot use for which variable.

    • For example, if you found the width and length of the rectangle are v cm and 7 cm, your formula will look like this: ${\displaystyle 5^{2}+7^{2}=c^{2}}$ .

11. xi

    Square the width and length, then add together these numbers together. Think, squaring a number means to multiply the number past itself.

12. 12

    Take the square root of each side of the equation. The easiest way to find a square root is to use a computer. Yous can use an online calculator if you practice not have a scientific calculator.^[16] This volition requite you the value of ${\displaystyle c}$ , which is the hypotenuse of the triangle, and the diagonal of the rectangle.

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Add New Question

• Question

  The diagonal of a rectangle is 25 cm. If one of the rectangle'south sides is 15 cm, how exercise I calculate the area?

  

  Use the Pythagorean Theorem to find the other side. Then multiply the length past the width.

• Question

  What is the diagonal if the width is 24' and the length is 20'?

  

  LyKaxandra Caimoy

  Customs Answer

  √[(24^2 )+(20^2)] = √576+400 = √976 = four√61`

• Question

  What is the diagonal measurement of a rectangle 150 anxiety in length by 100 anxiety in width?

  

  Use the Pythagorean Theorem (a^2 + b^2 = c^ii). A and B are the lengths of the two sides of the rectangle. To get the length of the hypotenuse, y'all would need to solve for C. C is the square root of (A squared plus B squared). And so c = (a^2 + b^2)^.5.

• Question

  A rectangular carpet has an area 120 square meters and a perimeter of 46 meters. How practise I detect its diagonal?

  

  The length plus the width equals one-half the perimeter (23). Let x equal the width. So (23 - x) is the length. Therefore, (ten)(23 - 10) = 120 (the area). Solve for x: (x)(23 - ten) = 23x - x² = 120. Then 23x - 10² - 120 = 0. Rewrite the equation slightly and multiply both sides by (-1): x² - 23x + 120 = 0. Cistron the left side: (x - 8)(ten - 15) = 0. ten = viii or xv. That means that the width of the rectangle is either 8 or 15, and the length is the other number. So the width is viii cm, and the length is 15 cm (because the length is defined as the longer dimension). Use the Pythagorean theorem to find the diagonal: 8² + 15² = the foursquare of the diagonal (d). So 64 + 225 = 289 = d², and d = 17 cm.

• Question

  How tin I observe the area of a rectangle if I only know its perimeter and diagonal?

  

  Because you cannot find the length and width of a rectangle if all yous know is the perimeter and the diagonal, y'all cannot calculate the area.

• Question

  How do I detect a square root?

  

  Most calculators have a foursquare root button. Yous can as well judge the value manually if you lot are familiar with perfect squares. For example, if y'all wanted to know the square root of 10, you would expect it to be between 3 and 4 since 10 is betwixt ix and 16 (the squares of three and 4, respectively). Y'all would also expect the square root to be closer to iii than 4, since 10 is much closer to 9 than to 16. (The reply is 3.16.)

• Question

  What are the iii points of contact for a ladder?

  

  Between two hands and two anxiety, you lot have iv potential contact points. To accept three contact points, means you either need to have two feet and one hand or ii hands and one foot in contact with the ladder at all times. If you are shifting from two anxiety and 1 manus in contact to one human foot and 2 hands in contact (or vice versa), you should e'er return to the two feet and 2 hands position get-go.

• Question

  What is the diagonal measurement for an area of 15.1 by xiii.0?

  

  If the length and width of a rectangle are 15.one past 13.0, and then you lot can use the pythagorean theorem to calculate the length of the diagonal since it forms a correct triangle. The pythagorean formula is a^2 + b^2 = c^two." Allow a=xv.1 and b=xiii. 15.one squared equals 228.01; 13 squared equals 169; add them together for 397.01. At present we know that c squared must equal 397.01. To solve for c, we take the foursquare root of 397.01, which is 19.925. This reply makes sense because it is longer than both the length and the width.

• Question

  How can I find the length of a rectangle by using the diagonal?

  

  LyKaxandra Caimoy

  Customs Reply

  At to the lowest degree one of the side of the rectangle must exist given to hands solve the length. You lot will just simply square the length given and subtract information technology to the foursquare of the diagonal. And so, get the square root of the divergence. The answer would exist the width (or the opposite side) of the rectangle.

• Question

  Tin can I piece of work out the length and width combinations if I know the diagonal?

  

  If the rectangle is a square, then yes. If the rectangle is not a square, then unfortunately no. If the rectangle is a square, then you can square the diagonal and divide past two to notice the area of the square. Then, by square rooting that value, you find the value of the side length.

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Article Summary X

To discover a measurement of a diagonal inside a rectangle, start past finding the rectangle's width and length. Side by side, foursquare the width and length and add them together. For example, if your rectangle is three cm wide and 4 cm long, foursquare these numbers to go 9 and 16. Add them to go 25, then find the square root of 25 to get five. Therefore, the measurement of the diagonal for your rectangle is 5 cm. To acquire more, including how to utilise expanse and perimeter to detect the measurement of a diagonal, coil down.

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Source: https://www.wikihow.com/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle

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